Significance of same frequency at different K values within photonic band gap

Using dispersion plot (ω Vs K), we can understand the nature of guided modes, present within the photonic band-gap. The photonic band-gap (PBG) appears since different discrete values of ω present at same K value.

How can I understand the phenomena, if at different K values there exist same value of ω, within PBG? for example, if the dispersion plot becomes parallel to the K axis at ω=ω0, a single frequency exist for all K values. How the frequency response should look like? Will there be single narrow spike at ω=ω0?

susovan0010 said:

The photonic band-gap (PBG) appears since different discrete values of ω present at same K value.

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This doens't necessarily mean there's a band gap. A band gap is given by the absence of any (real) K values in a certain range of ω. Different values of ω present at same K value just means there are multiple modes supported by the structure (or you're observing multiple Brillouin zones).

susovan0010 said:

How can I understand the phenomena, if at different K values there exist same value of ω, within PBG? for example, if the dispersion plot becomes parallel to the K axis at ω=ω0, a single frequency exist for all K values. How the frequency response should look like? Will there be single narrow spike at ω=ω0?

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Resonance. It means that the frequency of the mode is the same, regardless of K, as you'd expect from for example a LC resonator. Subsequently, yes -- the frequency response will generally have a narrow spike in this region (depending on the quality factor).

Thank you. It helps me lot.

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Different values of ω present at same K value just means there are multiple modes supported by the structure (or you're observing multiple Brillouin zones).[/QUOTE said:

We know wavelength and frequency are related with each other through c (velocity), By multiple modes, do you mean that the light with a single wavelength may propagate with different velocity? The change in velocity is reflected by the change in frequency since the wavelength is constant?

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susovan0010 said:

We know wavelength and frequency are related with each other through c (velocity)

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The point of k-ω diagrams is to examine a medium's dispersion. Only in a vacuum is light truly non-dispersive, in which k = ω/c.

susovan0010 said:

By multiple modes, do you mean that the light with a single wavelength may propagate with different velocity? The change in velocity is reflected by the change in frequency since the wavelength is constant?

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Yes. The medium will support multiple propagating modes at any given frequency, where each mode will have its own phase and group velocity profile.